BB guns I wouldn't shoot too much in a close confined area unless I constructed a special trap for the BB's.

BB's are pretty hard, and tend to bounce off lots of backstops and pellet traps. This is the thing about BB's - they don't deform on impact the way lead pellets or bullets do, so they tend to bounce back with quite a bit of their energy intact. So any backstop for a BB needs to soak up the energy from the BB. Something like foam rubber insulation mat that is 4" thick would do a good job of soaking up BB's.

I shoot air rifles and air pistols that shoot lead pellets indoors all the time. The backstops and pellet traps for these are very easy to make, or you could buy pellet traps.

Here's one example:

https://www.amazon.com/Do-All-Outdoors-Bullet-Rated-Caliber/dp/B000FDSUHC/ref=pd_cp_200_1?pd_rd_w=ddqf0&pf_rd_p=ef4dc990-a9ca-4945-ae0b-f8d549198ed6&pf_rd_r=WTVMDYQTT98R699T6TJ2&pd_rd_r=eb1aad49-17c9-11e9-9ab6-bffd06ef50b9&pd_rd_wg=garoj&pd_rd_i=B000FDSUHC&psc=1&refRID=WTVMDYQTT98R699T6TJ2#customerReviews

As you can see, you could make something like this. You could make it out of sheet steel - with pellet guns, you would not need any fancy armor steel (like AR400 or AR500) and you could weld something up pretty easily. The important thing to remember is to not make the angle of the backstop be too flat - ie, you really don't want the rear angle off the vertical to be more than about 40 degrees. You could get by quite nicely when 30 degrees. It is a misconception that bullets, when they hit a hard surface, ricochet off the surface an an angle equal to the incoming angle. ie, if you shot at a 45 degree angle to a plate of steel, you might think that the bullet is going to bounce off the steel at a 45 degree angle. In fact, this is not so - the bullet/pellet will tend to come off the plate at about 10 to 15 degrees.